# classic problem

An infinitely stretchable rubber band has one end nailed to a wall, while the other end is pulled away from the wall at the rate of 1 m/s; initially the band is 1 meter long. A bug on the rubber band, initially near the wall end, is crawling toward the other end at the rate of 0.001 cm/s. Will the bug ever reach the other end? If so, when?

give all ur views ..

1
Pavithra Ramamoorthy ·

the vel of d string gets transfered to d bug since its in contact wit the string.. when it acquires vel greater than that of the string the bug reaches the other end.. if ma answer is silly plz don mistake...

1
Rohan Ghosh ·

but the bug will not be able to acquire the velocity greater than that of the string

there will be some modification to that stament and u have to explain why

9
Celestine preetham ·

k
got that

(t+1)d =v(t2+t/2)

hence no solution for d=0

9
Celestine preetham ·

and yes t=0 is indeed a solution
therefore bug reaches wall at t=0(ie its alredy there)
note that if
dist from wall is 0 expansion vel is also 0
therefore bug reaches wall as soon as it starts

here i assumed d=0 though its not really

1
Rohan Ghosh ·

no celestine ..

there will be a t

9
Celestine preetham ·

then gimme initial dist of bug

1
Rohan Ghosh ·

initially the bug is at the wall end ..

9
Celestine preetham ·

come to chat mode

1
varun ·

Is it 105s ?

1
varun ·

I 'think' the dist of the bug from the wall at any sec is

dt = (.001+dt-1)*(t+1)/t cm.

62
Lokesh Verma ·

yes varun.. that is the right ans..

good work :)

1
skygirl ·

no the ans is (e^10^5-1)/1 â‰ˆ e^10^5..

9
Celestine preetham ·

rohan uve edited ur q :(
first u told that the direction of bug is opposite to one shown in pic
so i was calc time to reach the wall

and skygirls ans is right
even im gettin it

1
Rohan Ghosh ·

yes skygirl's ans is correct